by tommywallach Sun Oct 07, 2012 11:10 pm
Hey Nadia,
I don't have the books in front of me, but it sounds like you're asking for the probability that one will get more heads than tails when flipping a coin 5 times.
The easiest way to solve is to imagine that the odds of getting more heads than tails must be exactly the same as getting more tails than heads. There can't be a difference, given that there's never a better chance of getting heads than tails.
Or did I misunderstand your question?
-t
P.S. You seem to be counting 1T/4H as one possibility, where as 2T/3H is another possibility. But those two things don't have an equal probability of happening:
The ways to get 1T/4H: THHHH, HTHHH, HHTHH, HHHTH, HHHHT
The ways to get 2T/3H: TTHHH, THTHH, THHTH, THHHT, HTTHH,
HTHTH, HTHHT, HHTTH, HHTHT, HHHTT
See, there are only 5 ways to get 1T/4H, but 10 ways to get 2T/3H.
-t